Introduction to radians | Unit circle definition of trig functions | Trigonometry | Khan Academy

Understanding the definition and motivation for radians and the relationship between radians and degrees
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Trigonometry on Khan Academy: Big, fancy word, right? Don't be fooled. Looking at the prefix, tri-, you could probably assume that trigonometry ("trig" as it's sometimes called) has something to do with triangles. You would be right! Trig is the study of the properties of triangles. Why is it important? It's used in measuring precise distances, particularly in industries like satellite systems and sciences like astronomy. It's not only space, however. Trig is present in architecture and music, too. Now you may wonder...how is knowing the measurement and properties of triangles relevant to music?? THAT is a great question. Maybe you'll learn the answer from us in these tutorials!
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[@arjunsogarwal6099]

RAIDUSESESESESESESESESESESES, wow what a word

[@raithigovender195]

aw. I was so excited to comment RAAAADIUSSSES then I saw the comments section and was like...yeah nvm

[@slowloris2996]

I’m in the exact same situation.

[@lcveiris]

Ikr😂

[@ruguoserliegise2716]

same

[@stevedl3150]

I think radians should be taught from Primary School, rather than degrees. Radians are obviously intrinsic to the circle, whereas degrees are not. Alas, I still find it difficult to think in terms of radians.

[@lakshmipraba220]

Same!

[@kalaiselvanrajasekaran8352]

The concept is so easy yet it is still being a great task to understand the radians.

[@PenandPaperScience]

This is the core argument I make in my video covering Radians! It's a measure that incorporates only intrinsic properties of the circle!

[@isavenewspapers8890]

Have you heard of the number tau? It's represented with the Greek letter tau, which looks like this: τ τ is the ratio of a circle's circumference to its radius. This makes it 2 times π, or about 6.28. Using τ, one full rotation is τ radians. One-half of a full rotation is τ/2 radians. One-third of a full rotation is τ/3 radians. Whatever fraction of a full rotation you do, its measurement in radians is that same fraction of τ. If it helps, you can think of radians in terms of τ.

[@vsatrawada]

⁠

[@pboytrif1]

2:46 The moment I decided I liked the video... "I'm gonna attempt to draw a circle here....... *wobbly circle*...... not baaaaaad"

[@sirwaffle4006]

i never appreciate your circle drawing skills until i have to draw a circle myself

[@Jam-nh5wb]

U saying radiuseseseseseseseses drove me insane, I literally couldn’t pay attention to the video 😂

[@Faith._.M]

I was abt to say that

[@sarahkenza3883]

he literally wrote down the plural, it radians... IT'S RADIANS

[@Ferdinaand]

same and i was playing at 1.25 so it made it worse

[@BobBob-uv9fq]

Lol you’re correct ,but he’s explaining it well

[@furqaanilahi8078]

@@sarahkenza3883 radii?

[@saifullahrahman]

98% comments = radiuseseseses

[@olivermiller8943]

More like 60

[@The_Pariah]

That was a very good way of explaining this. I've been out of high school long enough to have forgotten a lot of trig. Now that I'm doing programming, this stuff is needed and these refresher videos really help (especially when they're well done like this one).

[@ellipszia]

radiuseseseseseseseseses

[@sunnylefabulous6736]

i knew from the moment our teacher started explaining this in class there'd be our lord and saviour, Sal Khan, who would explain this much, much better

[@XtremeKillah101]

radiuseseseseseses

[@tejasbinu5025]

What are RADIUESESESESE?

[@fantasaicproductions7612]

listen to that part at video speed x2 and you'll find out what it means... its means hes part snake or should i say slytherin....

[@LittleWhole]

Radii

[@timothycarney2951]

Radiuseseses?!? Radii! Radii! Radieye! RADI👁!

[@KaushalKumar-vq8kb]

Absolutely!

[@CreationTribe]

Yup - which is weird since I've heard him say "radii" multiple times in other videos. Is he just being funny? I don't get it.

[@user-ip9xi4ty9p]

very helpful! cracked me up every time he said radiuseseseses =)

[@alimuhammed9173]

RADIUESESESESE

[@feelgood_cinematic1919]

i thought i was the only one!!! lol

[@user-rf4vc7mt4d]

micheal jordan It's been a week, but... You don't have to watch it to understand, but it would definitely help

[@Neel-ff4mn]

2:23 To sum DEGREE! Lol!

[@ultrainstinctx6135]

Ali Muhammed I

[@roblox_pandagameryt8612]

Sub to me and i sub to u~

[@amrsaleh1342]

"just to show u this isn't voodo" 😂😂😂😂

[@ruguoserliegise2716]

Had me rolling

[@mischief9499]

hahahah

[@poochihuku3701]

The kinds of things that make me a stickler to learn from these videos

[@Cesariono]

The definition of the radian suddenly makes so much sense. I used radians in my calculations but I never really understood why they even bothered. Now my mind has been blown.

[@meightyalliu5408]

this video is clear! save my life from digging into textbook:P

[@DopeBoysClan]

I just had a "I UNDERSTAND" moment. I would have not resorted to these videos, along with the rest of the people here had teachers derived the meaning to mathematical concepts, instead of saying "here it is, use it". The amount of stupidity evident in today's education is absolutely mind-blowing, unfathomable. I can only but barley understand the teachers motives for not deriving and explaining where particular principles come from, that of which is they don't care, they want the paychecks and to go home. Fuck society man.

[@namraaah271]

where u from?how u doin now

[@valejandro1771]

@@namraaah271 HOPE he's ok. It's been a lot of time :0

[@benzonex]

radiuseseses...

[@yeo1913]

You haven't lost yet and you have more to achieve

[@herwin4946]

Thank you! I was so confused with the radian, but now I understand much more now.

[@bluewolf8085]

I learned alot today, Radiuseseseses are very important...😂😂😂😂

[@namraaah271]

if u still don't get it don't worry just read the textbook or whatever and keep trying to understand and then watch the video...i swear you'll get it.I have been spending the whole day trying to understand this and now i finally get it.time taken-approx 6 hours.dude...

[@tracker1312]

This was explained amazingly well. I don't think any of my teachers ever explained this, neither in grade school or college.

[@sourabhuwusingh]

A great explanation! Khan Academy is a great place to learn.

[@saflanix]

My teacher recorded a few videos during quarantine and I never watched them cuz these are so much better☺️

[@laxmandesai573]

I love the way u teach!! wish all the teachers were just like u

[@TechnicalGarg]

That was really nice. Many teachers just tell to remember this without informing about proper concept. But u r gr8.. Thank you a lot❤

[@svengunther7653]

Clear, easy, with background. Thanks :)

[@angmori172]

Awesome, thanks! Finally got radians!

[@rishab5501]

Nobody: Sal: I think it's intuitive, cause in an intuitive response I'll intuitively intuitive. Me: A video on what intuitive means?

[@jar0bi]

I'm taking a trigonometry class right now and this explains so much thank you

[@Propapanda0213]

Nice video! Straightforward and easy to understand

[@angelinoz5159]

Fantastic explanation. I study as well as teach physics. I couldn't have done it better myself. Congratulations.

[@callumsimpson1278]

What program do they use for the drawing?

[@MerlinZuni]

Thanks for this explanation. I'm taking a coding class and this was very helpful.

[@lucy2459]

thank you so much for making this so clear and being so friendly :) this really helped me. my maths teacher just gets angry when i don't understand things so stuff like this is a godsend :D

[@vsatrawada]

I was so focused in much in math that I forgot you teach like everything in the world.

[@yaronzaret9549]

Great video Sal, keep them coming!

[@MrWarmWeather]

great video. best I've seen on the subject so far. thanks!

[@ThomasGardner12321]

Thanks this is going to help me with my Core 2 A-level exams alot! :)

[@nitinchawla8854]

You made a good video...👍 Made me understand the radian concept.

[@johnydove4402]

this is great GOD BLESS

[@PenandPaperScience]

I wanted to plug my own video attempt where I explain this concept, but I have nothing to add. Great video! :D

[@saintisraelmedi7686]

This video very helpful. 👍🏻

[@EmpowerQuest1]

❤I know, the video was uploaded ten years ago but it had something that made me keep watching it till the end. ❤

[@gottfriedwiggles3230]

Very nice explanation! Thank you

[@frannylissetrodriguez4066]

Thank you so MUCH !

[@teenatkhan1695]

Thank Gosh this exists

[@theflash9735]

THIS IS SOOOOO GOOD !.... AND IT'S 7 YEARS AGO !!!!

[@pranjalpandey7020]

Great video really informative.Great Easter egg

[@chithienle9790]

your lectures are very easy to understan

[@noobtrader454]

how neatly u write on this is mind blown

[@aminmoafi5148]

Thank you!

[@drtoro]

how successfull are you to make things easier to understand..

[@samcaddy8544]

Explained brilliantly

[@charlieromeo7663]

Thanks for the explanation.

[@chissstardestroyer]

On the topic of using Pi in division; that in and of itself is usually why people round it to 3.14, to the hundredths place, otherwise it takes literally forever, or almost, to reach the termination point/end point, of the formula. As you pointed out, Mr. Khan, a very interesting way to convert them; actually you have a better time dividing by zero than dividing by pi to the final digit.

[@HuckleberryHim]

I got ~57.2957795131 degrees per radian using a calculator and pi as far as it would go (3.141592653589793).

[@271skippy]

I swear, I could never have gotten anywhere in math were it not for Khan Academy and Teaching Textbooks

[@yplayergames7934]

Even though it's a 11 years vídeo, this explained radians very well that I understand very clearly

[@Ash-ec4ip]

I respect u a lot.... Thank u❤️

[@mmohan692]

Wow nice video keep it up .

[@nikhilparaggarapinhilik4733]

He is good in explaining really Much better than me😫😂

[@calcul8er205]

Radii!!

[@poweruser64]

thanks for all the -radiuseses- radii

[@paras2901]

ur awesome!!!

[@harrisonriley16]

Great video

[@TheAmazingFocus]

He already did a video on Tau versus Pi. He probably doesn't want to introduce too much at once when introducing the concept of radians. Though an aside about it in a future angular measure would be nice!

[@waterwaterwa]

Thank you!!!!!!!!!!!!!

[@exceptionalchris]

"This isnt some voodoo" classic.

[@teenatkhan1695]

Chris Btw what is it😂

[@ramillax5478]

THANKS

[@JowieSterken]

Thanx mate, this is really helpful! =D

[@nabarungathiri6835]

u r great bro

[@Theiftanlazx]

yay i understand it much better

[@hazleenazlee506]

Thanks

[@Cryztaliser]

excellent video

[@fromexoplanet21]

Amazing👏👌

[@krishshah3974]

Having motivation behind ideas (rather than just memorizing them) makes Khan Academy amazing!

[@areeb9781]

amazingly explained. just wondering what radian is ? read some books but didn't get the satisfied answer and you really solved my problem. thanks for sharing :)

[@abdosalah4337]

So what is radian cuz i dont understand

[@6xsnspsychotik963]

god bless you guys

[@f4nte]

Nice.

[@mmohan692]

We want more videos like tz

[@SoundPeaks]

thanks, what tools allows you to make video like that? How do you draw and move mouse so precisely?

[@Ze0nite]

Spent my whole life thinking this was in fact some voodoo stuff and now I finally understand

[@Sadin15]

It is more commonly known as Arc Length. It is represented with an S and can be found using S = theta * radius

[@primaryaccount1410]

7:34 degrees-es-es

[@AndewMole]

On average he said "ses" 3.333 times. 4:32, 5:09, 5:50, 6:22, 6:44, 6:46, 7:07, 7:13, 8:36 4, 1, 5, 4, 3, 3, 5, 2, 3

[@vihaansinghhh3034]

6:23 RADIUSESESESESESESESESESESESESESEES..".... till 1 min 😂😂😂🤣

[@bilal2k1]

Genius

[@Achw3l]

Very well explained!! Logical and easy to follow :)

[@lemonrev]

radians something i dont think everyone is associated with the term and i like it how your thinking out side the box with the alien thing, with looking at circles, Do you think this actually should be the model for looking at degreese in general in stead of useing our term the degreese of ?

[@chissstardestroyer]

The Babylonians appear to have used a Base 12 numerical system, but 60 is equally easy to divide by the dozen as by the half-score, or by the full score.

[@rashedalam3450]

That's a better circle than i've ever drawn

[@chissstardestroyer]

If you divide by pi you'll be dividing forever, unless you abrieviate pi at some point, because pi is a non-terminating, non-repeating decimal, so it goes on and on forever. In fact, for many decades they've had computers just trying to calculate the termination of pi.

[@Sitara04]

do you have a video where you explain "complex" roots?

[@justTryin]

Why not just figure the angles based on the diameter so only 1 ×pi per circle

[@BareClause]

I thought u did this alreadyyy

[@imyasharya]

Hey Mr Sal Khan, would you tell me how can we draw 1 radian on paper?